Hi Peter,
As I mentioned on the Mathematica Users Forum, the general problem isn't well-defined: that's to say, given an ordered list of vertices, it's not in general possible to deduce what polyhedron this list is meant to specify.
The tetrahedron problem *is* well-defined. I don't think there's an inbuilt Mathematica function that does that (though I may be wrong), but it wouldn't be that hard to write your own. On the forum, I've posted a function I've called
tetrahedronByVertices
that does tetrahedra in this way.
Link to the forum page for this post:
http://www.mathematica-users.org/webMathematica/wiki/wiki.jsp?pageName=Special:Forum_ViewTopic&pid=6035#p6035
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